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Week
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Topics
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Study Metarials
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1
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Dirac delta function.
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2
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Delta shaped kernels I.
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3
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Delta shaped kernels II.
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4
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Singular integrals with delta shaped kernel
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5
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Properties of singular integrals with delta shaped kernel
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6
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Convergence of the family of singular integrals at characteristic points of the integrable functions
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7
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Rate of convergence of the family of singular integrals at characteristic points of the integrable functions
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8
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Convergence of integral operators of Fejer-type
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9
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Convergence of integral operators with radial kernels in multidimensional setting
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10
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Rate of convergence of integral operators of Fejer-type
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11
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Rate of convergence of integral operators with radial kernels in multidimensional setting
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12
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Some applications to Dirichlet problems I
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13
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Some applications to Dirichlet problems II
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14
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Some applications to Dirichlet problems III
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Prerequisites
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-
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Language of Instruction
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Turkish
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Responsible
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Assist. Prof. Dr. Gülsüm ULUSOY ADA
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Instructors
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1-)Doçent Dr. Gülsüm Ulusoy Ada
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Assistants
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-
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Resources
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1.) Deitmar A., (2005), A First Course in Harmonic Analysis.
2.) Pereyra M.C. and Ward L.A., (2012), Harmonic Analysis: From Fourier to Wavelets.
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Supplementary Book
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Hacıyev A., Deltasal Çekirdekli İntegral Operatörler, Lecture notes
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Goals
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This lecture deals with Dirac delta function, delta shaped kernels, singular integrals with delta shaped kernel, convergence and rate of convergence of the family of singular integrals at characteristic points of the integrable functions, convergence of integral operators of Fejer-type and integral operators with radial kernels in multidimensional setting, some applications to Dirichlet problems.
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Content
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Dirac delta function, delta shaped kernels, singular integrals with delta shaped kernel, convergence and rate of convergence of the family of singular integrals at characteristic points of the integrable functions, convergence of integral operators of Fejer-type and integral operators with radial kernels in multidimensional setting, some applications to Dirichlet problems.
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Program Learning Outcomes |
Level of Contribution |
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1
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Improve and deepen the gained knowledge in Mathematics in the speciality level
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5
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2
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Use gained speciality level theoretical and applied knowledge in mathematics
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5
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3
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Perform interdisciplinary studies by relating the gained knowledge in Mathematics with other fields.
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2
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4
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Analyze mathematical problems by using the gained research methods
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4
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5
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Conduct independently a study requiring speciliaty in Mathematics
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3
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6
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Develop different approaches and produce solutions by taking responsibility to problems encountered in applications
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5
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7
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Evaluate the gained speciality level knowledge and skills with a critical approach and guide the process of learning
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3
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8
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Transfer recent and own research related to mathematics to the expert and non-expert shareholders written, verbally and visually
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5
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9
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Make use of the necessary computer softwares and information technologies related to Mathematics
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-
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10
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Have the awareness of acting compatible with social, scientific, cultural and ethical values during the process of collecting, interpreting, applying and informing data related to Mathematics
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4
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